Losing Equilibrium: On the Existence of Abraham Wald's Fixed-Point Proof of 1935
33 Pages Posted: 29 Jul 2015
Date Written: July 27, 2015
In fall 1935, Abraham Wald presented an existence proof for a general equilibrium of exchange model to Karl Menger’s Mathematical Colloquium in Vienna. Due to limited space, the paper could not be printed in the eighth proceedings of the Colloquium (the Ergebnisse) published in spring 1937 but was scheduled for the ninth issue of the series. After the annexation of Austria to Nazi Germany in March 1938 however, Menger’s Colloquium ended and the proof never appeared in print. Nor did Wald, after he fled to the U.S. and launched a career in statistics, pursue the diffusion of his proof. Since the proof never appeared, there has been continued speculation about whether Wald’s missing proof employed a fixed-point theorem. To date this question has remained unanswered. After his sudden death in 1950, only Wald’s preliminary proof of 1934 was translated into English for Econometrica. When thus Arrow, Debreu, and McKenzie in 1954 referred in their own fixed-point proofs only to Wald’s preliminary published version, his 1935 proof was forgotten. This did not change when economists and historians of economics, the authors included, reconstructed Wald’s contribution. The authors’ new evidence, however, establishes that the missing proof employed a fixed-point theorem. This article tells the story of Wald’s lost equilibrium proof.
Keywords: Fixed-point theorem, general equilibrium theory, Vienna Mathematical Colloquium, Karl Menger, Abraham Wald
JEL Classification: B2, B3, C6
Suggested Citation: Suggested Citation